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A Chinese remainder theorem approach to skew generalized quasi-cyclic codes over finite fields

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Abstract

In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem in the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynomial, determine the dimension and give a lower bound on the minimum Hamming distance. The skew QC codes are also discussed briefly.

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Acknowledgments

The authors would like to thank the referees for their valuable suggestions. This research is supported by the National Key Basic Research Program of China (973 Program Grant No. 2013CB834204), the National Natural Science Foundation of China (Nos. 61171082 and 61301137)

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Correspondence to Jian Gao.

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Gao, J., Shen, L. & Fu, FW. A Chinese remainder theorem approach to skew generalized quasi-cyclic codes over finite fields. Cryptogr. Commun. 8, 51–66 (2016). https://doi.org/10.1007/s12095-015-0140-y

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